We investigate cascading failures in a class of scale-free coupled map lattices with a heterogeneity parameter. We found that for a network with given high heterogeneity, degree-based deliberate attack is much easier to trigger cascading failure than random attack. Furthermore, as the network becomes more heterogeneous, the network becomes more vulnerable to both random and deliberate attacks. Therefore, to avoid cascading failures in this kind of complex networks, the structure of the network should be as homogeneous as possible.